Risk Free Rate Formula

Article byWallstreetmojo Team
Edited byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

What is the Risk-Free Rate Formula?

A risk-free rate of return formula calculates the interest rate that investors expect to earn on an investment that carries zero risks, especially default risk and reinvestment risk, over some time. It is usually closer to the base rate of a Central Bank and may differ for the different investors. It is the rate of interest offered on sovereign or government bonds or the bank rate set by the country’s Central Bank. These rates are the function of many factors like – Rate of Inflation formulaRate Of Inflation FormulaThe rate of inflation formula helps understand how much the price of goods and services in an economy has increased in a year. It is calculated by dividing the difference between two Consumer Price Indexes(CPI) by previous CPI and multiplying it by 100.read more, GDP Growth rate, foreign exchange rate, economy, etc.

The risk-free rate of returnRisk-free Rate Of ReturnA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more is a key input in arriving at the cost of capitalCost Of CapitalThe cost of capital formula calculates the weighted average costs of raising funds from the debt and equity holders and is the total of three separate calculations – weightage of debt multiplied by the cost of debt, weightage of preference shares multiplied by the cost of preference shares, and weightage of equity multiplied by the cost of equity.read more and hence is used in the capital asset pricing modelCapital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more. This model estimates the required rate of return on investment and how risky the investment is compared to the total risk-free asset. It is used in the calculation of the cost of equityCalculation Of The Cost Of EquityCost of Equity (Ke) is what shareholders expect for investing their equity into the firm. Cost of equity = Risk free rate of return + Beta * (market rate of return - risk free rate of return). read more, which influences the company’s WACC.

Key Takeaways

  • Risk-free rate of return formula calculates investors’ expected interest rate on zero-risk investments, typically closer to a Central Bank’s base rate. It depends on factors like inflation, GDP growth, foreign exchange rate, and economy.
  • The risk-free rate of return is crucial for estimating capital cost, influencing asset price models, and calculating the cost of equity, impacting a company’s WACC.
  • Investors gain from an increased risk-free rate of return since it shows that the government is stable and confident. Companies may face pressure to boost stock prices to meet investors’ expectations for increased profits.

Below is the formula to derive the Cost of Equity using the risk-free rate of return using the model :

Financial Modeling & Valuation Courses Bundle (25+ Hours Video Series)

–>> If you want to learn Financial Modeling & Valuation professionally , then do check this ​Financial Modeling & Valuation Course Bundle​ (25+ hours of video tutorials with step by step McDonald’s Financial Model). Unlock the art of financial modeling and valuation with a comprehensive course covering McDonald’s forecast methodologies, advanced valuation techniques, and financial statements.

CAPM Model

Re = Rf+Beta (Rm-Rf)

Frequently Asked Questions (FAQs)

Is a higher risk-free rate better?

Additionally crucial for determining the Sharpe ratio is the risk-free rate. The risk-adjusted returns on a single security or an entire investment portfolio are assessed using this analytical method. The better the investment, the greater the ratio for both the CAPM and the Sharpe ratio.

What is the difference between the risk-free rate and the cost of capital?

The market’s risk-free rate plus a premium for the investment’s inherent risk determine the cost of capital. If investors were risk averse, the risk-free rate would be the proper discount rate for calculating the present value of projected net cash flows.

What is the difference between a risk-free rate and a risk premium?

Any return over the risk-free rate is considered a risk premium. The rate of return on an item or investment that, theoretically, carries no risk, such as a government bond, is the risk-free rate.

where,

However, It is usually the rate at which the government bonds and securities are available and inflation-adjusted. The following formula shows how to arrive at the risk-free rate of return:

Risk Free Rate of Return Formula = (1+ Government Bond Rate)/ (1+Inflation Rate)-1
Risk-Free-Rate-of-Return-Formula

This risk-free rate should be inflation-adjusted.

Explanation of the Formula

The various applications of the risk-free rate use the cash flows in real terms. Hence, the risk-free rate must also be brought to the same real terms, which is inflation-adjusted for the economy. Since the rate is mostly the long-term government bonds – they are adjusted to the rate of inflation factor and provided for further use.

The calculation depends upon the time period in evaluation.

Examples of instruments with Risk-Free Rates

The government of any country is assumed to have zero default riskDefault RiskDefault risk is a form of risk that measures the likelihood of not fulfilling obligations, such as principal or interest repayment, and is determined mathematically based on prior commitments, financial conditions, market conditions, liquidity position, and current obligations, among other factors.read more as they can print money to pay back their debt obligation as required. Therefore, the interest rate on zero-coupon government securities like Treasury BondsTreasury BondsA Treasury Bond (or T-bond) is a government debt security with a fixed rate of return and relatively low risk, as issued by the US government. You can buy treasury bonds directly from the US Treasury or through a bank, broker, or mutual fund company.read more, Bills, and Notes, are generally treated as proxies for the risk-free rate of return.

Examples of Risk-Free Rate of Return Formula (with Excel Template)

Let’s see some simple to advanced examples to understand it better.

You can download this Risk Free Rate of Return Formula Excel Template here – Risk Free Rate of Return Formula Excel Template

Example #1

Use the following data for the calculation of the risk-free rate of return.

  • 10 Year Government Bond Rate: 3.25%
  • Inflation Rate: 0.90%
  • Market Return: 6%
  • Beta: 1.5

The risk-free rate of return can be calculated using the above formula as,

Example 1.1png

=(1+3.25%)/(1+0.90%)-1

The answer will be – 

Risk Free Rate of Return Formula Example 1.2png

Risk-free Rate of Return = 2.33%

The cost of equity can be calculated using the above formula as,

Risk Free Rate of Return Formula Example 1.3png

=2.33%+1.5*(6%-2.33%)

Cost of Equity will be –

Example 1.4png

Cost of Equity = 7.84%

Example #2

Below is the information for India, for the year 2018

  • Rate of Inflation: 4.74%
  • 10 Year Government Bond: 7.61%

The risk-free rate of return can be calculated using the above formula as,

Example 2.1png

=(1+7.61%)/(1+4.74%)-1

The answer will be – 

Risk Free Rate of Return Formula Example 2.2png

Risk-free Rate of Return = 2.74%

Applications

The rate of return in India for the government securities is much higher than the U.S. rates for the U.S. Treasury. It is factored by the growth rate of each economy and the stage of development at which each stands. Therefore, the investors are shifting and considering investing in Indian government securities and bonds. The availability of such securities is easily accessible as well.

The largely used models involving the risk-free rate are:

The relevance of Risk-Free Rate of Return Formula

It can be seen from the two perspectives: the business and the investors’ perspective. From an investor’s point of view, a rising risk-free rate of return signifies a stable government, a confident treasury, and, ultimately, the ability to expect high returns on one’s investment. On the other hand, a rising risk-free rate scenario can be problematic for businesses. The companies would have to now meet the investors’ expectations of higher returns by improving stock prices. It might turn stressful as the business would now have to show good projections and have to thrive on meeting these profitabilityProfitabilityProfitability refers to a company's ability to generate revenue and maximize profit above its expenditure and operational costs. It is measured using specific ratios such as gross profit margin, EBITDA, and net profit margin. It aids investors in analyzing the company's performance.read more projections.

Recommended Articles

This article has been a guide to the Risk-Free Rate Formula. Here we discuss the calculation of a risk-free rate of return along with practical examples and downloadable excel templates. You may learn more about Valuations from the following articles –

Reader Interactions

Leave a Reply

Your email address will not be published. Required fields are marked *